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Displaying 81 – 100 of 133

On the global maximum of the solution to a stochastic heat equation with compact-support initial data

Mohammud Foondun, Davar Khoshnevisan (2010)

Annales de l'I.H.P. Probabilités et statistiques

Consider a stochastic heat equation ∂tu=κ ∂xx2u+σ(u)ẇ for a space–time white noise ẇ and a constant κ>0. Under some suitable conditions on the initial function u0 and σ, we show that the quantities lim sup t→∞t−1sup x∈Rln El(|ut(x)|2) and lim sup t→∞t−1ln E(sup x∈R|ut(x)|2) are equal, as well as bounded away from zero and infinity by explicit multiples of 1/κ. Our proof works by demonstrating quantitatively that the peaks of the stochastic process x↦ut(x) are highly concentrated...

On the Hopfield algorithm. Foundations and examples.

Popoviciu, Nicolae, Boncuţ, Mioara (2005)

General Mathematics

On the interior boundary-value problem for the stationary Povzner equation with hard and soft interactions

Vladislav A. Panferov (2004)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

The Povzner equation is a version of the nonlinear Boltzmann equation, in which the collision operator is mollified in the space variable. The existence of stationary solutions in $L^{1}$ is established for a class of stationary boundary-value problems in bounded domains with smooth boundaries, without convexity assumptions. The results are obtained for a general type of collision kernels with angular cutoff. Boundary conditions of the diffuse reflection type, as well as the given incoming profile, are...

On the Landau approximation in plasma physics

R Alexandre, C Villani (2004)

Annales de l'I.H.P. Analyse non linéaire

On the Lawrence–Doniach model of superconductivity: magnetic fields parallel to the axes

Stan Alama, Lia Bronsard, Etienne Sandier (2012)

Journal of the European Mathematical Society

We consider periodic minimizers of the Lawrence–Doniach functional, which models highly anisotropic superconductors with layered structure, in the simultaneous limit as the layer thickness tends to zero and the Ginzburg–Landau parameter tends to infinity. In particular, we consider the properties of minimizers when the system is subjected to an external magnetic field applied either tangentially or normally to the superconducting planes. For normally applied fields, our results show that the resulting...

On the Lax-Phillips scattering theory for transport equation

Hassan Emamirad (1984)

Journées équations aux dérivées partielles

On the minimizers of the Ginzburg-Landau energy for high kappa : the axially symmetric case

Amandine Aftalion (1999)

Annales de l'I.H.P. Analyse non linéaire

On the mixed even-spin Sherrington–Kirkpatrick model with ferromagnetic interaction

Wei-Kuo Chen (2014)

Annales de l'I.H.P. Probabilités et statistiques

We study a spin system with both mixed even-spin Sherrington–Kirkpatrick (SK) couplings and Curie–Weiss (CW) interaction. Our main results are: (i) The thermodynamic limit of the free energy is given by a variational formula involving the free energy of the SK model with a change in the external field. (ii) In the presence of a centered Gaussian external field, the positivity of the overlap and the extended Ghirlanda–Guerra identities hold on a dense subset of the temperature parameters. (iii) We...

On the modified Enskog equation for elastic and inelastic collisions. Models with spin

Maria J. Esteban, Benoit Perthame (1991)

Annales de l'I.H.P. Analyse non linéaire

On the motion of a body in thermal equilibrium immersed in a perfect gas

Kazuo Aoki, Guido Cavallaro, Carlo Marchioro, Mario Pulvirenti (2008)

ESAIM: Mathematical Modelling and Numerical Analysis

We consider a body immersed in a perfect gas and moving under the action of a constant force. Body and gas are in thermal equilibrium. We assume a stochastic interaction body/medium: when a particle of the medium hits the body, it is absorbed and immediately re-emitted with a Maxwellian distribution. This system gives rise to a microscopic model of friction. We study the approach of the body velocity V(t) to the limiting velocity $V_{\infty}$ and prove that, under suitable smallness assumptions, the approach...

On the multiple overlap function of the SK model.

Sergio de Carvalho Bezerra, Samy Tindel (2007)

Publicacions Matemàtiques

In this note, we prove an asymptotic expansion and a central limit theorem for the multiple overlap R1, ..., s of the SK model, defined for given N, s ≥ 1 by R1, ..., s = N-1Σi≤N σ1i ... σsi. These results are obtained by a careful analysis of the terms appearing in the cavity derivation formula, as well as some graph induction procedures. Our method could hopefully be applied to other spin glasses models.

On the NLS dynamics for infinite energy vortex configurations on the plane.

f. bethuel, r. l. jerrard, d. smets (2008)

Revista Matemática Iberoamericana

On the non-convexity of the time constant in first-passage percolation.

Kesten, Harry (1996)

Electronic Communications in Probability [electronic only]

On the number of fully packed loop configurations with a fixed associated matching.

Caselli, F., Krattenthaler, C., Lass, B., Nadeau, P. (2004)

The Electronic Journal of Combinatorics [electronic only]

On the number of ground states of the Edwards–Anderson spin glass model

Louis-Pierre Arguin, Michael Damron (2014)

Annales de l'I.H.P. Probabilités et statistiques

Ground states of the Edwards–Anderson (EA) spin glass model are studied on infinite graphs with finite degree. Ground states are spin configurations that locally minimize the EA Hamiltonian on each finite set of vertices. A problem with far-reaching consequences in mathematics and physics is to determine the number of ground states for the model on $ℤ^{d}$ for any $d$ . This problem can be seen as the spin glass version of determining the number of infinite geodesics in first-passage percolation or the number...